The present invention is concerned with methods for fabricating nanostructures to develop a band gap, and elementary particle emission properties.
Semiconductors, or semiconducting materials, have a small energy band gap (about one eV or less) between the conduction band and the valence band associated with the solid. This gap in energy distribution is useful for microelectronics such as lasers, photodetectors, and tunnel junctions. Intrinsic semiconductors (not doped by another element) conduct due to the effect that raising the temperature will raise the energy of some electrons to reach the conduction band. Intrinsic semiconductors usually have a very low conductivity, due to the difficulty of exciting an electron by approximately one eV.
Silicon is a commonly used semiconducting material and has limited electrical conductivity. In using silicon, designers of semiconductor devices are bound by the inherent material limitations of silicon.
The electrical conductivity of a semiconducting material is enhanced by adding small amounts of impurities, such as gallium arsenide. However, the process by which dopants are implanted in a semiconductor substrate of a semiconductor device is expensive and time-consuming. Also, the designing of semiconductor devices using doped materials currently known in the art, such as silicon and gallium arsenide, often requires a lengthy and expensive trial and error process to achieve the desired band gap.
From the foregoing, it may be appreciated that a need has arisen for a band gap material that does not require doping, or materials having other characteristics, to produce a desired band gap, and a method for making such a band gap material.
It is well known in quantum mechanics that elementary particles have wave properties as well as corpuscular properties. The probability of finding an elementary particle at a given location is |ψ|2 where ψ is a complex wave function and has form of a de Broglie wave, as follows:ψ=A exp[(−i2π/h)(Et−pr)]  (1)
where h is Planck's constant; E is an energy of the particle; p is an impulse of the particle; r is a vector connecting initial and final locations of the particle; and t is time.
There are well known fundamental relationships between the parameters of this probability wave and the energy and the impulse of the particle.
The wave number k related to the impulse of the particle as follows:p=(h/2π)k  (2)
The de Broglie wavelength, λ, is given by:λ=2π/k  (3)
At zero time, t=0, the space distribution of the probability wave may be obtained. Accordingly, substituting (2) into (1) gives:ψ=A exp(ikr)  (4)
FIG. 1 shows an elementary particle wave moving from left to right perpendicular to a surface 104 dividing two domains. The surface is associated with a potential barrier, which means the potential energy of the particle changes as it passes through it.
Incident wave 101 Aexp(ikx) moving towards the border will mainly reflect back as reflected wave 103 βAexp(−ikx), and only a small part leaks through the surface to give transmitted wave 102 α(x)Aexp(ikx) (β≈1>>α). This is known as quantum mechanical tunneling. The elementary particle will pass the potential energy barrier with a low probability, depending on the potential energy barrier height.
Usagawa in U.S. Pat. No. 5,233,205 discloses a novel semiconductor surface in which interaction between carriers such as electrons and holes in a mesoscopic region and the potential field in the mesoscopic region leads to such effects as quantum interference and resonance, with the result that output intensity may be changed. Shimizu in U.S. Pat. No. 5,521,735 discloses a novel wave combining and/or branching device and Aharanov-Bohm-type quantum interference devices which have no curved waveguide, but utilize double quantum well structures.
Mori in U.S. Pat. No. 5,247,223 discloses a quantum interference semiconductor device having a cathode, an anode and a gate mounted in vacuum. Phase differences among the plurality of electron waves emitted from the cathode are controlled by the gate to give a quantum interference device operating as an AB type transistor.
In U.S. patent application Ser. No. 09/020,654, filed Feb. 9, 1998, entitled “Method for Increasing Tunneling through a Potential Barrier”, Tavkhelidze teaches a method for promoting the passage of elementary particles at or through a potential barrier comprising providing a potential barrier having a geometrical shape for causing de Broglie interference between said elementary particles.
Referring to FIG. 2, two domains are separated by a surface 201 having an indented shape, with height a. An incident probability wave 202 is reflected from surface 201 to give two reflected waves. Wave 203 is reflected from top of the indent and wave 204 is reflected from the bottom of the indent. The reflected probability wave will thus be:
                                          A            ⁢                                                  ⁢                          βexp              ⁡                              (                                  -                  ikx                                )                                              +                      A            ⁢                                                  ⁢                          βexp              ⁡                              [                                  -                                      ik                    ⁡                                          (                                              x                        +                                                  2                          ⁢                          a                                                                    )                                                                      ]                                                    ⁢                                  =                  A          ⁢                                          ⁢                                    βexp              ⁡                              (                                  -                  ikx                                )                                      ⁢                                                  [                          1              +                              exp                ⁡                                  (                                      -                    ik2a                                    )                                                      ]                                              (        5        )            
When k2a=π+2πn, exp(−iπ)=−1 and equation (5) will equal zero.
Physically this means that for k2a=(2π/λ)2a=π+2πn and correspondingly a=λ(1+2n)/4, the reflected probability wave equals zero. Further this means that the particle will not reflect back from the border. Leakage of the probability wave through the barrier will occur with increased probability and will open many new possibilities for different practical applications.
Indents on the surface should have dimensions comparable to the de Broglie wavelength of an electron. In particular the indent height should be:a=nλ/2+λ/4  (6)
Here n=0, 1, 2, etc., and the indent width should be on the order of 2λ. If these requirements are satisfied, then elementary particles will accumulate on the surface.
For semiconductor material, the velocities of electrons in an electron cloud is given by the Maxwell-Boltzman distribution:F(v)dv=n(m/2πKBT) exp(−mv2/2 KBT)dv  (7)
where F(v) is the probability of an electron having a velocity between v and v+dv.
The average velocity of the electrons is:Vav=(3 KBT/m)1/2  (8)
and the de Broglie wavelength corresponding to this velocity, calculated using formulas (2), (3) and the classical approximation p=mv is:λ=h/(3m KBT)1/2=62 Å for T=300K.  (9)
This gives a value for a of 62/4=15.5 Å. Indents of this depth may be constructed on a surface by a number of means known in the art of micro-machining. Alternatively, the indented shape may be introduced by depositing a series of islands on the surface.
In metals, free electrons are strongly coupled to each other and form a degenerate electron cloud. Pauli's exclusion principle teaches that two or more electrons may not occupy the same quantum mechanical state: their distribution is thus described by Fermi-Dirac rather than Maxwell-Boltzman. In metals, free electrons occupy all the energy levels from zero to the Fermi level (εf)
Probability of occupation of energy states is almost constant in the range of 0–εf and has a value of unity. Only in the interval of a few KBT around εf does this probability drop from 1 to 0. In other words, there are no free states below εf. This quantum phenomenon leads to the formal division of free electrons into two groups: Group 1, which comprises electrons having energies below the Fermi level, and Group 2, comprising electrons with energies in the interval of few KBT around εf.
For Group 1 electrons, all states having energies a little lower or higher are already occupied, which means that it is quantum mechanically forbidden for them to take part in current transport. For the same reason electrons from Group 1 cannot interact with the lattice directly because it requires energy transfer between electron and lattice, which is quantum mechanically forbidden.
Electrons from Group 2 have some empty energy states around them, and they can both transport current and exchange energy with the lattice. Thus only electrons around the Fermi level are taken into account in most cases when properties of metals are analyzed.
For electrons of Group 1, two observations may be made. The first is that, if one aims to create a physical surface structure to achieve electron wave interference, it is substantially easier to fabricate a structure for Group 1 electron wave interference, since their wavelength of 50–100 Å corresponds to about 0.01εf, (E˜k2˜(1/λ)2). Group 2 electrons of single valence metals, on the other hand, where εf=2–3 eV, have a de Broglie wavelength of around 5–10 Å, which is much smaller and more difficult to fabricate.
The second observation is that for quantum mechanical interference between de Broglie waves to take place, the mean free path of the electron should be large. Electrons from Group 1 satisfy this requirement because they effectively have an infinite mean free path due to their very weak interaction with the lattice and impurities within the lattice.
If an electron from Group 1 has k0=π/2a and energy ε0, and is moving to the indented surface 201. As discussed above, this particular electron will not reflect back from the surface due to interference of de Broglie waves, and will leave the metal in the case where the potential barrier is such type that allows electron tunneling (e.g. an electric field is applied from outside the metal or there in another metal nearby).
Consider further that the metal is connected to a source of electrons, which provides electron 2, having energy close to εf (Group 2). As required by the thermodynamic equilibrium, electron 2 will lose energy to occupy state ε0, losing energy εf−ε0, for example by emission of a photon with energy εp=(εf−ε0). If this is absorbed by electron 3, electron 3 will be excited to a state having energy εf+εp=2εf−ε0.
Thus as a consequence of the loss of electron 1, electron 3 from the Fermi level is excited to a state having energy 2εf−ε0, and could be emitted from the surface by thermionic emission or tunnel trough potential barrier. The effective work function of electron 3 is reduced from the value of Φ to Φ−εf+ε0=Φ−(εf−ε0). In other words, the work function of electron 3 is reduced by εf−ε0.
Thus indents on the surface of the metal not only allow electron 1 to tunnel with high probability by interference of the de Broglie wave, but also result in the enhanced probability of another electron emission (electron 3) by ordinary thermionic emission. The present invention deals with methods for constructing such a surface.
In the case that the potential barrier does not allow tunneling, the indented surface creates electron de Broglie wave interference inside the metal, which leads to the creation of a special region below the fermi energy level. Inside that region, the number of possible quantum states is dramatically decreased so that it could be regarded as an energy gap.
Thus this approach has a two-fold benefit. Firstly, providing indents on a surface of a metal creates for that metal a band gap, and secondly, this approach will decrease the effective potential barrier between metal and vacuum (the work function) in the case that the potential barrier is of such a type that an electron can tunnel through it.
This approach has many applications, including applications usually reserved for conventional semiconductors. Other applications include cathodes for vacuum tubes, thermionic converters, vacuum diode heat pumps, photoelectric converters, cold cathode sources, and many other in which electron emission from the surface is used.
In addition, an electron moving from vacuum into an anode electrode having an indented surface will also experience de Broglie interference, which will promote the movement of said electron into said electrode, thereby increasing the performance of the anode.
The development of low-cost, high-throughput techniques that can achieve resolutions of less than 50 nm is essential for the future manufacturing of semiconductor integrated circuits and the commercialization of electronic, opto-electronic, and magnetic nanodevices. Numerous technologies are under development. Scanning electron beam lithography has demonstrated 10 nm resolution; however, because it exposes point by point in a serial manner, the current throughput of the technique is too low to be economically practical for mass production of sub-50 nm structures. X-ray lithography has demonstrated 20 nm resolution in a contact printing mode and can have a high throughput, but its mask technology and exposure systems are currently rather complex and expensive. Lithographies based on scanning proximal probes, which have shown a resolution of about 10 nm, are in the early stages of development.
Conventional e-beam lithography involves exposing a thin layer of resist (usually a polymer film) coated on a metal film, itself deposited on a substrate, to an electron beam. To create the desired pattern in the resist, the electron beam is scanned across the surface in a predetermined fashion. The chemical properties of the resist are changed by the influence of the electron beam, such that exposed areas may be removed by a suitable solvent from the underlying metal film. The surface of the exposed metal film is etched, and finally unexposed resist is removed by another solvent.
In the etching process, the isotropic properties of the metal mean that the etchant will etch in both depth and in a direction parallel to the substrate surface under the resist. The depth of etching under the resist is approximately the same as the thickness of the metallic film.
If this approach is used to create two metal strip lines which are as narrow as possible and separated by a minimum possible distance, then the under-etching means that the width of strip is decreased and the distance between the strips is increased. In addition, part of the resist under-etched can collapse, which makes the edge of the strip irregular, or break during subsequent fabrication steps.
Overall, this means that the width of the strip is less than desired, and the distance between the strips is more than planned. Very thin strips can be produced, but the minimum distance between strips is greater than wanted. In another words, strips can be made which are even less wide than the e-beam focusing dimension, but distance between strips is greater than expected. In addition non-regularities on the strip edges are obtained.
One approach to overcome the under-etch is focused ion beam (FIB) processing. This approach is described in U.S. Pat. No. 4,639,301 to Doherty et al., and uses an apparatus which makes possible the precise sputter etching and imaging of insulating and other targets, using a finely focused beam of ions. This apparatus produces and controls a submicron beam of ions to precisely sputter etch the target. A beam of electrons directed on the target neutralizes the charge created by the incident ion beam. The FIB system can precisely deposit either insulating or conducting materials onto an integrated circuit. However, this approach requires each item to be produced separately, and consequently is slow and expensive.
Another approach to creating nano-structures is described by Chou et al., Science, Volume 272, Apr. 5, 1996, pages 85 to 87, entitled “Imprint Lithography with 25-nanometer Resolution.” Chou et al. demonstrate an alternative lithographic method, imprint lithography, that is based on compression molding and a pattern transfer process. Compression molding is a low-cost, high-throughput manufacturing that provides features with sizes of >1 μm which are routinely imprinted in plastics. Compact disks based on imprinting in poly-carbonate are one example. Other examples are imprinted polymethylmethacrylate (PMMA) structures with a feature size on the order of 10 μm and imprinted polyester patterns with feature dimensions of several tens of micrometers. However, compression molding has not been developed into a lithographic method to pattern semiconductors, metals, and other materials used in semiconductor integrated circuit manufacturing.
Chou's approach uses silicon dioxide molds on a silicon substrate. The mold was patterned with dots and lines having a minimum lateral feature size of 25 nm by means of electron beam lithography, and the patterns were etched into the SiO2 layer by fluorine-based RIE. This mold is pressed into a thin PMAA resist cast on a substrate, which creates a thickness contrast pattern in the resist. After the mold is removed, an anisotropic etching process is used to transfer the pattern into the entire resist thickness by removing the remaining resist in the compressed areas. This imprinted PMAA structure has structures with 25 nm feature size and a high aspect ratio, smooth surfaces with a roughness of less than 3 nm and corners with nearly 90° angles. The structures, though of little use in nano-electronic devices, are useful as masters in a lift off process for making nano-structures in metals: 5 nm of Ti and 15 nm of Au are deposited onto the entire sample, and then the metal on the PMMA surface is removed as the PMMA is dissolved in acetone.
Chou's approach thus requires two stages to produce the finished metal structure: first, nanoimprint lithography into a polymer mold; and second, a metal lift-off and reactive ion etch. The number of steps used will clearly bear on the difference between the original mold and the final product. In addition, the lift-off process destroys the polymer mold, which means that a new PMAA mold must be produced in each process cycle.